At the bottom is a completed addition problem, with all the digits replaced by letters. Every letter represents a single digit and different letters represent different digits. Which digit might the letter T represent. MH + MH MH = TM

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17-05-2021
Mathematics

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At the bottom is a completed addition problem, with all the digits replaced by letters. Every letter represents a single digit and different letters represent different digits. Which digit might the letter T represent. MH + MH MH = TM

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lshi lshi · Answer 1 · 2021-05-20T04:03:53+02:00

Answer:

T = 5 (H = 7, M = 1); T = 7 (H = 4, M = 2); T = 9 (H = 1, M = 3)

Step-by-step explanation:

We know MH+MH+MH=TM

MH is a two digit number, and TM is also a two digit number.

MH+MH+MH=3*(MH)<100

3M<=9, meaning that M could be 1, 2, or 3.

If M=1, MH+MH+MH=3(10+H)=30+3H=TM=10*T+1

30+3H=10T+1, so 3H must include 1 in one's digit.

The only possibility is that 3H = 21, then H = 7

MH+MH+MH=17+17+17=TM=51, T = 5

If M=2, MH+MH+MH=3(20+H)=60+3H=TM=10T+2

60+3H=10T+2, so 3H must include 2 in one's digit.

The only possibility is 3H = 12, then H = 4

MH+MH+MH=24+24+24=72, T = 7

If M=3, MH+MH+MH=3(30+H)=90+3H=TM=10T+3

90+3H=10T+3, so 3H must include 3 in one's digit.

The only possibility is 3H = 3, then H =1

MH+MH+MH=31+31+31=93, T=9

facundo3141592 facundo3141592 · Answer 2 · 2022-04-20T14:38:15+02:00

We will see that if we define M = 2, and H = 4, the value that T takes is T = 7

Which digit the letter T represent?

We know that:

MH + MH + MH = TM

We can write this as:

M*10 + H + M*10 + H + M*10 + H = T*10 + M

30*M + 3*H = T*10 + M

30*M - M + 3*H = T*10

(29*M + 3*H)/10 = T

Now we need to find two values for M and H such that T is a digit.

For example, if M = 2 we have:

(29*2 + 3*H)/10 = T

(58 + 3*H)/10 = T

Now we can take H = 4, then we get:

(58 + 3*4)/10 = T

(58 + 12)/10 = T = 7

In this case, we found that a possible value of T is T = 7.

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